Solve sqrt{8}+2sqrt[4]{1/3}-(sqrt{27}-sqrt{2})

$$\sqrt { 8 } + 2 \sqrt[ 4 ] { \frac { 1 } { 3 } } - ( \sqrt { 27 } - \sqrt { 2 } )$$

Evaluate

$$\frac{2\times 3^{\frac{3}{4}}}{3}+3\sqrt{2}-3\sqrt{3}\approx 0.566159636$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+2\sqrt[4]{\frac{1}{3}}-\left(\sqrt{27}-\sqrt{2}\right)$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$2\sqrt{2}+2\sqrt[4]{\frac{1}{3}}-\left(3\sqrt{3}-\sqrt{2}\right)$$

To find the opposite of 3\sqrt{3}-\sqrt{2}, find the opposite of each term.

$$2\sqrt{2}+2\sqrt[4]{\frac{1}{3}}-3\sqrt{3}+\sqrt{2}$$

Combine 2\sqrt{2} and \sqrt{2} to get 3\sqrt{2}.

$$3\sqrt{2}+2\sqrt[4]{\frac{1}{3}}-3\sqrt{3}$$